This paper is the first part of a Marxian critique of the theory of the firm focusing on the analysis of labour values. Starting from Adam Smith-s example of the deer hunter, marginal analysis is introduced culminating in the derivation of the Labour Value Function as the supply curve of the competitive firm in terms of labour values. The analysis is based on a new definition of labour value which is Marxian in spirit and respects modern mathematical optimization methods not found in Marx and offers a further development and coherent interpretation of Marx-s value theory. The analysis is limited to the case of the competitive firm.